Since I am a mathematician I don’t easily scare, at least I am not scared by statistical terminology. Still, it is hard to remember the difference between

sensitivity, specificity

positive and negative predictive value

likelihood ratios

So I tried to find a good example to study these and came up with jolt accentuation for suspected bacterial meningitis. In short, jolt accentutation means (exacerbation of) headache upon 2/sec head turns and is purported to be more sensitive than neck stiffness by the first publication and by this JAMA evidence based medicine review. To get some real data, we used a tiny collection of Iranian patients and then started constructing the four-field-table.

Here is the grid:

True positive

False positive

Test positive

False negative

True negative

Test negative

Diseased

Healthy

All

And here are the formulas:

Sensitivity: TP / (TP + FN)

Specificity: TN / (FP + TN)

Positive predictive value: TP / (TP + FP)

Negative predictive value: TN / (FN + TN)

Positive likelihood ratio: TP / FP
= sensitivity / (1 – specificity)

Negative likelihood ratio: FN / TN
= specificity / (1 – sensitivity)

Want more?

You can use the likelihood ratios to calculate the posttest odds from the pretest odds: post odds = pre odds * likelihood ratio. Problem is: you need to use odds rather than probabilities and we usually don’t. Of course: odds = probability / (1 – probability) and conversely probability = odds / (1 + odds). If it’s too much of a hassle, use a calculator on your IPhone or use Fagan’s nomogram.

Likelihood ratios are independant of disease prevalence – all the info about the disease goes into the pretest probability.

[…] of which the core is Bayes theorem. Now we had a session once that covered the intricacies of odds vs. probabilities in using Bayes theorem, but perhaps it is more in order to discuss the theorem itself, so that is […]